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Free quasi-symmetric functions, product actions and quantum field theory of partitions. (English) Zbl 1187.05079

Summary: We investigate two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender’s QFT (quantum field theory) of partitions. We end by exploring possibilities to construct noncommutative analogues.

MSC:

05E05 Symmetric functions and generalizations
11P81 Elementary theory of partitions
81T18 Feynman diagrams
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